This invention relates to investigation of earth formations and, more particularly, to a method and apparatus for obtaining properties of earth formations using sonic logging and determining anisotropic and shear moduli and related characteristics of the earth formations.
It is well known that mechanical disturbances can be used to establish acoustic waves in earth formations surrounding a borehole, and the properties of these waves can be measured to obtain important information about the formations through which the waves have propagated. Parameters of compressional, shear, and Stoneley waves, such as their velocity (or its reciprocal, slowness) in the formation and in the borehole, can be indicators of formation characteristics that help in evaluation of the location and/or producibility of hydrocarbon resources.
An example of a logging device that has been used to obtain and analyze sonic logging measurements of formations surrounding an earth borehole is called a Dipole Shear Sonic Imager (xe2x80x9cDSIxe2x80x9d-trademark of Schiumberger), and is of the general type described in Harrison et al., xe2x80x9cAcquisition and Analysis of Sonic Waveforms From a Borehole Monopole And Dipole Source For The Determination Of Compressional And Shear Speeds And Their Relation To Rock Mechanical Properties And Surface Seismic Dataxe2x80x9d, Society of Petroleum Engineers, SPE 20557, 1990. In conventional use of the DSI logging tool, one can present compressional slowness, xcex94tc, shear slowness, xcex94ts, and Stoneley slowness, xcex94tst, each as a function of depth, z. [Slowness is the reciprocal of velocity and corresponds to the interval transit time typically measured by sonic logging tools.]
An acoustic source in a fluid-filled borehole generates headwaves as well as relatively stronger borehole-guided modes. A standard sonic measurement system consists of placing a piezoelectric source and an hydrpohone receivers inside a fluid-filled borehole. The piezoelectric source is configured in the form of either a monopole or a dipole source. The source bandwidth typically ranges from a 0.5 to 20 kHz. A monopole source generates primarily the lowest-order axisymmetric mode, also referred to as the Stoneley mode, together with compressional and shear headwaves. A dipole source primarily excites the lowest-order flexural borehole mode together with compressional and shear headwaves. The headwaves are caused by the coupling of the transmitted acoustic energy to plane waves in the formation that propagate along the borehole axis. An incident compressional wave in the borehole fluid produces critically refracted compressional waves in the formation. Those refracted along the borehole surface are known as compressional headwaves. The critical incidence angle xcex8i=sinxe2x88x921(Vf/Vc), where Vf is the compressional wave speed in the borehole fluid; and Vc is the compressional wave speed in the formation. As the compressional headwave travels along the interface, it radiates energy back into the fluid that can be detected by hydrophone receivers placed in the fluid-filled borehole. In fast formations, the shear headwave can be similarly excited by a compressional wave at the critical incidence angle xcex8i=sinxe2x88x921(Vf/Vs), where Vs is the shear wave speed in the formation. Headwaves are excited only when the wavelength of the incident wave is smaller than the borehole diameter so that the boundary can be effectively treated as a planar interface. In a homogeneous and isotropic model of fast formations, as above noted, compressional and shear headwaves can be generated by a monopole source placed in a fluid-filled borehole for determining the formation compressional and shear wave speeds. It is known that refracted shear headwaves cannot be detected in slow formations (where the shear wave velocity is less than the borehole-fluid compressional velocity) with receivers placed in the borehole fluid. In slow formations, formation shear velocities are obtained from the low-frequency asymptote of flexural dispersion. There are standard processing techniques for the estimation of formation shear velocities in either fast or slow formations from an array of recorded dipole waveforms.
Both the monopole and dipole waveforms recorded at an array of receivers can be processed by a modified matrix pencil algorithm that isolates non-dispersive and dispersive arrivals in the wave train (Ekstrom, 1995). The compressional headwave velocity is the formation quasi-compressional (qP-) wave velocity along the borehole axis. The low-frequency asymptote of the lowest-order axisymmetric Stoneley dispersion yields the tube wave velocity (VT) along the borehole axis. The formation quasi-shear (qSV-) and shear (SH-) velocities are obtained from the low-frequency asymptotes of the two orthogonally polarized borehole flexural waves propagating along the borehole axis.
Among the areas of interest in the background of the present invention is the field of seismic prospecting. Seismic prospecting for hydrocarbon reserves requires estimates of all the five transversely isotropic (TI-) anisotropic constants of overburden shale for reliable identification and location of target reservoirs. Shale typically constitutes more than 70% of the formation that a borehole trajectory passes through before reaching the target reservoir. Consequently, if the proper anisotropic constants of shale are not accounted for in the velocity model, it is more probable that drilling based on seismic prospecting will miss the target reservoir.
Sedimentary rocks frequently possess an anisotropic structure resulting, for example, from thin bedding, fine scale layering, the presence of oriented microcracks or fractures or the preferred orientation of nonspherical grains or anisotropic minerals. This type of anisotropy is called formation intrinsic anisotropy. A dipole dispersion crossover is an indicator of stress-induced anisotropy dominating any intrinsic anisotropy that may also be present.
Failure to properly account for anisotropy in seismic processing may lead to errors in velocity analysis, normal moveout (NMO) correction, dip moveout (DMO) correction, migration, time-to-depth conversion and amplitude versus offset (AVO) analysis. The main cause of anisotropy in sedimentary basins is the presence of shales which, as noted above, typically form a major component of the basin (Jones et al., 1981), and overlie many hydrocarbon reservoirs. Shales are anisotropic as a result of layering and a partial alignment of plate-like clay minerals (Jones et al., 1981; Sayers, 1994). This anisotropy may be described, to a good approximation, as being transversely isotropic (TI). A TI medium is invariant with respect to rotations about a symmetry axis and may be described by five independent elastic stiffnesses. An example is a sedimentary rock for which the bedding plane is a plane of isotropy.
AVO analysis requires some combinations of formation anisotropic constants. Some of these constants can be obtained from the borehole sonic measurements, others can be obtained from borehole seismic measurements, such as walk-away VSPs. The elastic constants that can be obtained from the borehole sonic measurements are the three formation shear moduli and a compressional modulus from the compressional headwave logging.
It is among the objects of the present invention to provide technique and apparatus for obtaining further information about characteristics of anisotropic formations and more complete and accurate determination of formation attributes.
Shales in sedimentary basins usually exhibit velocity anisotropy characterized by a TI-symmetry with the symmetry axis in the vertical direction. For dipping beds, the axis may be tilted with respect to the vertical, often to be perpendicular to the sedimentary layering. When the important TI-constants of shale in a basin are known, the quasi-compressional (qP-), quasi-shear (qSV-), and shear (SH-) wave velocities can be calculated as a function of deviation angle from the TI-symmetry axis.
In the prior art, borehole sonic measurements provide estimates of two formation shear moduli in anisotropic formations by a borehole flexural logging probe, such as the above-referenced DSI tool. These shear moduli are in the two sagittal planes passing through the borehole axis and the two orthogonal radial directions. The shear modulus obtained by a monopole source in the refracted shear headwave logging is an azimuthal average of the two formation shear moduli in the sagittal planes. Existing applications of the Stoneley logging that employs a low-frequency monopole source are in the estimation of either formation permeability or fractures intersecting the borehole assuming the formation to be effectively isotropic. A third formation shear modulus in the plane perpendicular to the borehole axis can be obtained from the low-frequency asymptote of the borehole Stoneley dispersion. The Stoneley dispersion can be obtained by processing the monopole waveforms by a somewhat broadband low-frequency source. Together with the two formation shear moduli obtained by the flexural logging probe, this technique provides the three anisotropic shear moduli of the formation by the inversion of DSI/BCR and Stoneley mode acquisitions. The three anisotropic shear moduli can help in indentifying (1) Isotropic formationsxe2x80x94characterized by c44=c55=c66; (2) VTI formations (TI formations with vertical axis of symmetry)xe2x80x94characterized by c44=c55xe2x89xa0c66 (X3-symmetry axis); (3) HTI formations (TI formations with horizontal axis of symmetry)xe2x80x94characterized by c44xe2x89xa0c55=c66 (X1-symmetry axis); and (3) Orthorhombic formationsxe2x80x94characterized by c44xe2x89xa0c55xe2x89xa0c66. These shear moduli together with associated formation anisotropy are useful indicators of the existing formation fractures, layerings, and relative magnitudes of formation principal stresses. For instance, a VTI formation anisotropy in a vertical wellbore can be an indicator of horizontal fractures and layerings or formation stresses characterized by SHmax=Shminxe2x89xa0SV, where SHmax, Shmin, and SV are the maximum horizontal, minimum horizontal, and vertical stresses. Similarly, a HTI formation anisotropy in a vertical wellbore can be an indicator of vertical fractures and layerings or formation stresses characterized by SV=SHmaxxe2x89xa0Shmin. An isotropic formation can be an indicator of isotropic formation stresses SV=SHmax=Shmin. In contrast, an orthorhombic formation can be an indicator of two orthogonal fracture systems or formation stresses characterized by SVxe2x89xa0SHmaxxe2x89xa0Shmin. In addition, it can be an indicator of aligned fractures or formation stresses to be obliquely oriented with respect to the borehole axes. The tangential compliance of a fractured formation and stress parameters of a prestressed formation can also be estimated from the three shear moduli. These moduli are also needed in the amplitude versus offset (AVO) analysis of seismic surveys of anisotropic formations.
In accordance with a form of the invention, a method is set forth for determining properties of a transverse isotropic (e.g. shaly) region of earth formations traversed by a wellbore having, substantially vertical and deviated sections therethrough, comprising the following steps: measuring sonic velocity properties in formations surrounding the substantially vertical section of the wellbore; measuring sonic velocity properties in formations surrounding the deviated section of the wellbore; and determining, from the measured velocities in the substantially vertical and deviated sections of the formations, all of the transverse isotropic elastic constants of the formation region. [As used herein the term xe2x80x9ctransverse isotropicxe2x80x9d is intended to include formations that are substantially transverse isotropic.] In an embodiment of this form of the invention, the step of measuring sonic velocity properties in formations surrounding the substantially vertical section of the wellbore includes measuring compressional, shear, and tube wave velocities of the formations. In a further embodiment, the step of measuring sonic velocity properties in formations surrounding the deviated section of the wellbore includes measuring the shear, quasi-shear, and tube wave velocities in formations surrounding the deviated section of the wellbore. Also, an embodiment of the invention further includes the step of determining the azimuth xcfx86 and deviation xcex8 from the transverse isotropic axis of the wellbore trajectory in the deviated section of the well bore, and the determination of elastic constants of the region is also a function of the azimuth xcfx86 and deviation xcex8.
In accordance with a further form of the invention, a method is set forth for determining properties of a transverse isotropic (e.g. shaly) region of earth formations traversed by a wellbore having a deviated section therethrough, comprising the following steps: measuring sonic velocity properties in formations surrounding the deviated section of the wellbore; determining the ratio of axial to radial components of polarization associated with quasi-compressional or quasi-shear waves in formations surrounding the deviated section of the wellbore; and determining, from the measured velocities and the determined ratio in the deviated sections of the formations, all of the transverse isotropic elastic constants of the region.
An embodiment of the invention further includes the step of determining the wellbore fluid mass density and compressional velocity, and the determination of elastic constants of the region of formations is also a function of the wellbore fluid mass density and compressional velocity.
In accordance with another form of the invention, a method is set forth for determining properties of a region of earth formations that is transverse isotropic with vertical axis of symmetry, traversed by a wellbore having a substantially deviated section therethrough, comprising the following steps: measuring compressional velocity in formations surrounding the substantially deviated section of wellbore; measuring two orthogonally polarized shear velocities in the formations surrounding the substantially deviated section of wellbore; and determining three elastic parameters of the formations surrounding the substantially deviated section of wellbore.
In accordance with still another form of the invention, a method is set forth for determining properties of a region of earth formations having orthorhombic or monoclinic symmetry with respect to a wellbore traversing the region of formations, comprising the following steps: measuring two orthogonally polarized shear velocities in formations surrounding the wellbore in the region; measuring the tube wave velocity in formations surrounding the wellbore in the region; and determining, from the measured shear velocities and tube wave velocity, three shear moduli referred to the wellbore axis, of the region of formations.
Further features and advantages of the invention will become more readily apparent from the following detailed description when taken in conjunction with the accompanying drawings.